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Published in:
An Introduction to Digital Chaotic Systems Updated by Random Iterations Read chapter Read first chapter

2018 | OriginalPaper | Chapter

5. Higher-Dimensional Digital Chaotic Systems (HDDCS)

Authors : Qianxue Wang, Simin Yu, Christophe Guyeux

Published in: Design of Digital Chaotic Systems Updated by Random Iterations

Publisher: Springer International Publishing

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Abstract

Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, quantization is inevitable for digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This chapter aims at developing a novel methodology to design higher-dimensional digital chaotic systems (HDDCS) on the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy Devaney’s definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via the field programmable gate array (FPGA) platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.

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previous chapter One-Dimensional Digital Chaotic Systems (ODDCS)
next chapter Investigating the Statistical Improvements of Various Chaotic Iterations-Based PRNGs
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Metadata
Title
Higher-Dimensional Digital Chaotic Systems (HDDCS)
Authors
Qianxue Wang
Simin Yu
Christophe Guyeux
Copyright Year
2018
Book
Design of Digital Chaotic Systems Updated by Random Iterations

Print ISBN: 978-3-319-73548-1

Electronic ISBN: 978-3-319-73549-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-73549-8_5